Common Core Standards Grade Level: 8 Domain: Functions Cluster: Define, Evaluate, and Compare Functions Standards:
1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
3. Interpret the equation y = mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
What understandings are desired?
Students will understand that:(U)
• a function is a rule that assigns to each input exactly one output.
• functions have properties that can be represented algebraically, graphically, or verbally.
• the equation y=mx+b defines a linear function (straight line) and the constant of proportion (m) is the slope.
What essential questions will be considered?
Essential Questions:(Q)
• Why is there an input for every output when evaluating functions?
• How can you solve systems of two linear equations?
• How can you explain y=mx+b?
What key knowledge and skills will students acquire as a result of this unit?
Students will know:(K)
Students will be able to:(S)
• Terminology: Slope, linear equation, linear function, x-cordinate,
y-cordinate, origin, y-intercept form
• Formulas: y=mx+b, slope, y-intercept, input/output table
• Critical Details: Express relationship between two quantities,
interpret components of relationship (slope and y-intercept), tables,
understanding graphs
• show functions can be represented algebraically, graphically and verbally
• evaluate slope (m) as the constant of proportion
• test for every input into a function so that there is an output
• argue a function is a rule
• relate linear functions and equations and slope to solve problems and analyze situations
• recognize y=mx+b defines a linear function (straight line)
Stage 1 - Identify Desired Results
Grade Level: 8
Domain: Functions
Cluster: Define, Evaluate, and Compare Functions
Standards:
1. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
3. Interpret the equation y = mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
What understandings are desired?
• functions have properties that can be represented algebraically, graphically, or verbally.
• the equation y=mx+b defines a linear function (straight line) and the constant of proportion (m) is the slope.
What essential questions will be considered?
• How can you solve systems of two linear equations?
• How can you explain y=mx+b?
What key knowledge and skills will students acquire as a result of this unit?
y-cordinate, origin, y-intercept form
• Formulas: y=mx+b, slope, y-intercept, input/output table
• Critical Details: Express relationship between two quantities,
interpret components of relationship (slope and y-intercept), tables,
understanding graphs
• evaluate slope (m) as the constant of proportion
• test for every input into a function so that there is an output
• argue a function is a rule
• relate linear functions and equations and slope to solve problems and analyze situations
• recognize y=mx+b defines a linear function (straight line)
2004 ASCD and Grant Wiggins and Jay McTighe.